Question: Simplify the following expression: $k = \dfrac{x^2 - 13x + 30}{x - 10} $
Solution: First factor the polynomial in the numerator. $ x^2 - 13x + 30 = (x - 10)(x - 3) $ So we can rewrite the expression as: $k = \dfrac{(x - 10)(x - 3)}{x - 10} $ We can divide the numerator and denominator by $(x - 10)$ on condition that $x \neq 10$ Therefore $k = x - 3; x \neq 10$